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Re: sufficent proof for primes of the kind p:=x^2+x+1

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  • Dario Alpern
    ... as ... But p=241 is not congruent to 3 (mod 4). So it is not a counter- example. Best regards, Dario Alpern Buenos Aires - Argentina
    Message 1 of 3 , Dec 13, 2006
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      --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>
      wrote:
      >
      > --- In primenumbers@yahoogroups.com, "Bernhard Helmes" <bhelmes@>
      > wrote:
      > >
      > > A beautifull evening,
      > >
      > > I try to give you a sufficent proof for primes p:=x^2+x+1
      > >
      > > p:=x^2+x+1=x*(x+1)+1 with p = 3 mod 4 => 2 appears only one time
      as
      > > divisor of p-1
      > > p mod 3 = 1 or in other words 3 | p-1
      > > p mod 9 > 1 => 3 appears only one time as divisor of p-1
      > >
      > > 2 ^ ((p-1)/2) = p-1 mod p, must be verified
      > >
      > > then p is prime
      > >
      >
      > Hi, Bernhard.
      > I think that x=15 is a counter-example... 2^((240/2)) == 1 mod 241.
      > Is it? Bill
      >

      But p=241 is not congruent to 3 (mod 4). So it is not a counter-
      example.

      Best regards,

      Dario Alpern
      Buenos Aires - Argentina
      http://www.alpertron.com.ar/ENGLISH.HTM
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